• Rafael Martínez-GuerraEmail author
  • Oscar Martínez-Fuentes
  • Juan Javier Montesinos-García
Part of the Mathematical and Analytical Techniques with Applications to Engineering book series (MATE)


This chapter contains introductory concepts to ring theory, beginning with basic definitions, followed by the definitions of ideals, homomorphisms and rings, then isomorphism theorems in rings are given, next properties about integer rings are introduced and finally polynomial rings are explained.


  1. 1.
    Birkhoff, G., Mac Lane, S.: A Survey of Modern Algebra. Universities Press (1965)Google Scholar
  2. 2.
    Dummit, D.S., Foote, R.M.: Abstract Algebra, vol. 3. Hoboken, Wiley (2004)Google Scholar
  3. 3.
    Fraleigh, J.B.: A First Course in Abstract Algebra. Addison-Wesley (2003)Google Scholar
  4. 4.
    Lang, S.: Algebra. Springer (2002)Google Scholar
  5. 5.
    Saracino, D.: Abstract Algebra: A First Course. Waveland Press (2008)Google Scholar
  6. 6.
    Herstein, I.N.: Abstract Algebra. Prentice Hall (1996)Google Scholar
  7. 7.
    Hungerford, T.W.: Abstract Algebra: An Introduction. Cengage Learning (2012)Google Scholar
  8. 8.
    Jacobson, N.: Lectures in Abstract Algebra, vol. 1. Van Nostrand, Basic concepts (1951)Google Scholar
  9. 9.
    Kunz, E.: Introduction to Commutative Algebra and Algebraic Geometry. Birkhuser (1985)Google Scholar
  10. 10.
    Samuel, P., Serge, B.: Mthodes d’algbre abstraite en gomtrie algbrique. Springer (1967)Google Scholar
  11. 11.
    Herstein, I.N.: Topics in Algebra. Wiley (2006)Google Scholar
  12. 12.
    Bourbaki, N.: Commutative Algebra, vol. 8. Hermann, Paris (1972)Google Scholar
  13. 13.
    Zariski, O., Samuel, P.: Commutative Algebra, vol. 1. Springer Science & Business Media (1958)Google Scholar
  14. 14.
    Zariski, O., Samuel, P.: Commutative Algebra, vol. 2. Springer Science & Business Media (1960)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Rafael Martínez-Guerra
    • 1
    Email author
  • Oscar Martínez-Fuentes
    • 1
  • Juan Javier Montesinos-García
    • 1
  1. 1.Departamento de Control AutomáticoCINVESTAV-IPNMexico CityMexico

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